In the United States, a physician will usually (though not always) take a swab of the throat or nose of a patient with flu-like illness. This swab is sent to the clinical laboratory where a "rapid" test is performed. The rapid test is somewhat inexpensive and quick, but it is not very accurate. During the peak of the flu season, rapid tests are most accurate in helping to diagnose a flu infection.
After the rapid test is done, the swab may be forwarded to a reference or Public Health laboratory for PCR and tissue culture. PCR is a test that determines what genetic material is present in the sample, and so it detects the RNA of the flu virus. Once that RNA is detected, a few computer algorithms help the laboratorian determine the type (A, B, or C) of influenza virus and the subtype (H1 through H9) of the virus. Further PCR testing can then help to detect genes specific for "swine" flu... Which, by the way, will now be "officially" called the "2009 H1N1 influenza virus", according to CDC.